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The Graham-Diaconis inequality shows the equivalence between two well-knownmethods of measuring the similarity of two given ranked lists of items:Spearman's footrule and Kendall's tau. The original inequality assumesunweighted items in input lists. In this paper, we first define versions ofthese methods for weighted items. We then prove a generalization of theinequality for the weighted versions.

A Weighted Generalization of the Graham-Diaconis Inequality for Ranked List Similarity